English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We revisit Ito's \cite{I1989} natural extension of the Farey tent map, whichgenerates all regular continued fraction convergents and mediants of a givenirrational. With a slight shift in perspective on the order in which theseconvergents and mediants arise, this natural extension is shown to provide anelegant and powerful tool in the metric theory of continued fractions. A wealthof old and new results -- including limiting distributions of approximationcoefficients, analogues of a theorem of Legendre and their refinements, and ageneralisation of L\'evy's Theorem to subsequences of convergents and mediants-- are presented as corollaries within this unifying theory.

A unifying theory for metrical results on regular continued fraction convergents and mediants